High-temperature phase transitions in SrHfO₃: A Raman scattering study

In the search for gate oxides to replace oxidized Si, emphasis of late has been on SrHfO₃. As shown by IBM [1], this is a nearly optimal material with EOT (equivalent oxide thickness) $< 1\ \text{nm}$ and reasonable channel mobility. Rossel et al. [2] observed that the channel mobility in SrHfO₃-based n-FET increases by post processing annealing but the EOT also at the cost of change in equivalent oxide thickness due to interfacial regrowth. Considerable efforts have been made in determining the crystal phases at different temperatures [3], and calculating the electronic structure in comparison with SrTiO₃. The high-temperature phase transitions at ca. 670 K and 1023 K are important not only as examples of vibrational instabilities ("soft modes") and pretty spectroscopy, but also they lie in the temperature region in which real gate-oxide devices are annealed in normal processing. Thus, understanding and controlling these transitions can improve the final product, for example by optimizing the oxygen vacancy concentration. We show below that the upper transition near 1023 K is second order (or very nearly so) and displacive, which means that there is little or no thermal hysteresis or latent heat and that the structure does not become disordered in normal annealing (which is anywhere from 700 to 1450 K) [4,5]. Any disordering would degrade channel mobility in SHO-based n-FET and probably the dielectric constant of the final film, whereas a first-order transition might produce cracking.

In the present work, spectra of SrHfO₃ have been successfully obtained at temperatures from 300 to 1073 K. Significant softening of both branches of the soft phonon modes which become doubly degenerate in the tetragonal $(I4/mcm)$ phase above 1023 K is observed. The primitive unit cell doubles below 1023 K in the orthorhombic $(Cmcm)$ phase, and a twofold degenerate zone-boundary soft mode in the high-temperature phase becomes Raman active and nondegenerate, splitting into a B_1g branch ($107\ \text{cm}^{-1}$ at room temperature) and an A_g branch at $232\ \text{cm}^{-1}$ (ambient). It is found that the damping constant of soft mode satisfies a universal scaling theory $\gamma (T)=\gamma (0)\times t^{-n}$, where t is the reduced temperature and $n =1/2$, as in other pseudocubic displacive ferroelectrics.

Within the perovskite family with general formula $\text{A}^{2+}\,\text{B}^{4+}\,\text{O}_{3}^{2-}$ (A = Sr, Ca, Ba and B = Hf, Ti, Sn, Zr), the 5d band insulator SrHfO₃ is currently the subject of intensive investigation, because it offers a whole range of applications in microelectronics, high-k materials, microwave ceramics resonators [6–10]. At room temperature, SrHfO₃ belongs the space group $D_{2h}^{16}\ (Pbnm)$ containing four formula units [11]. In addition, such perovskite materials undergo a variety of structural phase transitions, ranging from antiferrodistortive to ferroelectric and antiferroelectric involving the rotation of BO₆ octahedra around the three O–B–O crystallographic axes. They provide the simplest examples of a unit-cell doubling transition [11] with temperature and pressure, which make them very interesting to understand the physics underlying staggered phase transitions [11–21]. Kennedy et al. [11] studied the crystal structure at high temperatures using powder neutron diffraction and sequences of phase transitions in SrHfO₃ take place as

$$\begin{eqnarray*} &\mathop{\text{Orthorhombic}}_{(\textit{Pbnm})} \mathop{\leftrightarrow}^{(673\text{-}873\ \text{K})} \mathop{\text{Orthorhombic}}_{(\textit{Cmcm})} \mathop{\leftrightarrow}^{(873\text{-}1023\ \text{K})} &\mathop{\text{Tetragonal}}_{(I4/\textit{mcm})} \mathop{\leftrightarrow}^{(1360\ \text{K})} \mathop{\text{Cubic}}_{(Pm3m)}. \end{eqnarray*}$$

Not all investigators have used these correct structures; for example de la Presa assumed [22] a $Pnma\text{-}Imma$ transition near 700 K instead of the two-step $Pbnm\text{-}Cmcm\text{-}I4/mcm$ sequence shown above. In addition, neutron diffraction data [11] also show that the atomic displacements clearly implicate a soft mode of the anion in the transition which may be responsible for ferroelectric instability in SrHfO₃. In order to study the ferroelectric instability in SrHfO₃, Fabricius et al. [23] presented the electronic-structure calculations of cubic SrTiO₃ and SrHfO₃. They stated that the tendency to ferroelectricity of both compounds is explored and compared by displacing the transition metal atom ∼Ti⁴⁺ or Hf⁴⁺ towards one of the oxygens along the [001] direction, and showed that ferroelectricity is more favoured in SrTiO₃ with respect to SrHfO₃. This fact may be correlated with the degree of hybridization between transition metal d-O p bands, as has been found for other related systems. They [23] further pointed out that owing to the determined unstable mode, SrHfO₃ presents also a strong tendency to ferroelectricity. However, this instability may compete with the low-temperature orthorhombic phase probably associated with a nonpolar zone-boundary soft mode. Moreover, Stachiotti et al. [24] calculated the zone-center phonon frequencies and eigenvectors of cubic SrHfO₃ and noted an unstable ferroelectric mode in SrHfO₃ with completely different displacement pattern as obtained for SrTiO₃. Vali et al. [25] investigated the existence of antiferrodistortive (AFD) instability in the cubic perovskite structure of SrHfO₃ but do not reveal any tendency to ferroelectricity in a cubic phase. More recently, Murata et al. [26] predicted the appearance of soft-mode optical phonons in $I4/mcm$ and at the Γ-point in Cmcm; and the atomic displacements for the soft mode are analogous to those of the R₂₅ mode of Pm3m, which is related to the rotation of the HfO₆ octahedron.

SrHfO₃ was prepared by employing a solid-state reaction method [21]. The nominal composition of powder SrCO₃ (99.99%) and HfO₂ (99.99%) was mixed by a mechanical ball milling process for 24 hours. The mixture obtained was pressed into a disc-shaped pellet. The disc was sintered at 1650 K for 24 h. To examine the ambient structure of the cooled specimens, theta–2-theta $(\theta\text{-}2\theta)$ x-ray diffraction (XRD) experiments were carried out, and the observed X-ray diffraction indicates the formation of single-phase orthorhombic perovskite structure with the space group $Pbnm\ (D_{2h}^{16})$ similar to the XRD pattern reported by Kennedy et al. [16]. Raman scattering spectra were obtained using a T64000 spectrometer (JobinYvon) equipped with a triple-grating monochromator with additive dispersion and a green YAG-laser at 532 nm. The measurements were performed with a micro-Raman option using a photomultiplier (R464S). The Raman signal was analyzed by employing normal back-scattering geometry. The spectral resolution was typically less than $1\ \text{cm}^{-1}$. A microscope-compatible heating/cooling stage was used for recording the temperature-dependent spectra.

At room temperature SrHfO₃ is characterized by orthorhombic symmetry with the space group $Pbnm\ (D_{2h}^{16})$. The group-theoretical analysis indicates that the following 24 modes are Raman active among 60 zone-center (Γ-point) phonon modes [20]:

$$\begin{equation*} \Gamma_{\textit{Pbnm}} =7 A_{g} +5 B_{1g} +7 B_{2g} +5 B_{3g}. \end{equation*}$$

Raman scattering spectra of the orthorhombic SrHfO₃ were measured in the back-scattering geometry at a temperature range from 300 to 1073 K. Most of the twenty-four Raman-active modes were observed in the Raman spectrum at room temperature. At room temperature we observed a total of 15 Raman modes: four sharp peaks appeared at 144, 166, 424 and $599\ \text{cm}^{-1}$; and other peaks appearing at 107, 116, 128, 134, 232, 282, 324, 405, 453, 502, 651, $682\ \text{cm}^{-1}$ are relatively weak in intensity. Most of the Raman frequencies are exactly the same as the results reported by Park et al. [27]. Comparing these observed values with the Raman peaks observed previously [27] and the theoretically calculated results in SrHfO₃ [26], one can conclude that the two lowest phonon modes at $107\ \text{cm}^{-1}$ and $232\ \text{cm}^{-1}$ at room temperature are assigned as B_1g and A_g modes, respectively, as shown in fig. 1.

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In order to account for the accurate value of the phonon frequencies and linewidths of these Raman modes at different temperatures (i.e., correcting peak positions for damping), we used the damped harmonic-oscillator (DHO) model to fit the Raman profiles as reported by Samanta et al. [28]

$$\begin{equation*} I(\omega )=\frac{\chi_{0}\Gamma_{0}\omega\omega_{0}^{2}(\overline{n\left(\omega \right)}+1)}{(\omega_{0}^{2}-\omega^{2})^{2}+\omega^{2}\Gamma_{0}^{2}}, \end{equation*}$$

where $n(\omega) = \exp(-\hbar\omega/k_{B} T)-1$ is the phonon occupation number, $\omega_{0}$ the mode frequency, $\Gamma_{0}$ the linewidth, and $\chi_{0}$ is the oscillator strength and shown in figs. 2 and 3.

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As the temperature increases from 823 to 1023 K, we observe a remarkable change in low-frequency Raman modes at around 107 and $232\ \text{cm}^{-1}$ (room temperature frequencies). Upon heating, the two modes show softening and disappear or become overdamped near 1023 K. The lowest optical mode at $({\sim}107\ \text{cm}^{-1})$ shows considerable softening (down to 60 cm⁻¹ from ambient to 1023 K and they gradually coalesce into broad Rayleigh wings as shown in fig. 1(a). The A_g soft-mode branch at $232\ \text{cm}^{-1}$ also undergoes a similar change, and disappears/overdamps above 1023 K, as clearly shown in fig. 1(b). At 1023 K SrHfO₃ undergoes a slightly first-order displacive phase transition from $Cmcm\ (D_{2h}^{14})$ with eight formula units per primitive cell to a $I4/mcm$ space group lattice with four formula units per primitive cell.

We interpret this pair of soft modes as the two components of a single doubly degenerate soft mode at the Brillouin zone boundary of the high-temperature tetragonal phase, made Raman active by the new Brillouin zone that arises in the low-temperature phase by the unit cell doubling below 1023 K. This transition is very similar to the ferroelectric phase transition in O-18 SrTiO₃ from tetragonal to orthorhombic [29–33] or possibly tetragonal to triclinic [31–33]. It is interesting to note that upon heating the intensity of the soft phonon mode at $107\ \text{cm}^{-1}$ increases, whereas the intensities of other Raman modes decrease with temperature, and hence the temperature dependence of the soft mode can be clearly observed. These temperature dependences can be attributed to a single cell-doubling antiferrodistortive temperature-induced soft-mode phase transition near 1023 K.

The temperature dependence of the mode frequency and the FWHM of the lowest Raman mode at $107\ \text{cm}^{-1}$ are shown in figs. 2(a) and (c), and the square of the mode frequency is shown in fig. 2(b). The solid line indicates the temperature dependence of the form $\omega =\text{const} \times (T_{c}-T)^{\alpha}$, where $T_{c}=1151\ \text{K}$ and $\alpha = 0.50$ as presented in fig. 2(a). In fig. 2(b), we find that the temperature dependence of the B_1g soft mode obeys the Curie-Weiss law $[\omega^{2}\alpha (T -T_{c} )]$. Figure 2(c) presents the damping constant (γ) of soft modes as a function of temperature and increased towards the phase transition temperature. Figure 2(d) shows that the soft mode γ/γ(0) vs. the reduced temperature $t\ (t=(T_{c} -T)/T_{c})$ satisfies the "universal" scaling theory [34] $\gamma (T)=\gamma (0)\times t^{-n}$, $(n =0.50 \pm 0.03)$, where the scaling constant $\gamma (0)$ is equal to the linewidth at the lowest temperature.

Figure 3 shows the temperature dependence of the mode frequency of the A_g soft mode at $232\ \text{cm}^{-1}$. Figure 3(a) presents the frequency $(\omega)$ vs. temperature T (K) for $232\ \text{cm}^{-1}$ and we observed the fitting parameters $\alpha = 0.50$ for $T_{c} =1151\ \text{K}$ which reveals that the temperature evolution of two soft phonon modes is similar to the lowest soft phonon mode at $107\ \text{cm}^{-1}$ (at ambient temperature). Figure 3(b) presents $(\omega^{2})$ vs. temperature for the A_g mode. The solid line in fig. 3(b) describes a temperature dependence of the form $\omega^{2}=\omega_{T_{c}}^{2} +a(T -T_{c})$, where $\omega_{T_c}^{2} =24957\ \text{cm}^{-2}$, $a=34.0\ \text{cm}^{-2}/\text{K}$ and $T_c = 1151\ \text{K}$. The damping constant $(\gamma)$ of soft modes as a function of temperature and increased is presented in fig. 3(c). Figure 3(d) presents γ/γ(0) vs. reduced temperature $(t)$ and we observed $n=0.48 \pm 0.03$, which reveals that the change in the damping constant for the A_g soft mode at $232\ \text{cm}^{-1}$ also follows the same "universal" scaling. We conclude that the transition is actually first order. This is based upon the fact that the best least squares fit to the soft mode gives T_c about 1151 K above the actual transition temperature, implying a small discontinuity. It is possible that the transition is nearly tricritical. Other measurements, such as precise calorimetry of specific heat, would clarify this question. The transition according to symmetry could be second order, since it appears to satisfy a group-subgroup relationship.

These two soft modes originate from the triply degenerate F_2u mode in a prototypic cubic phase such as room temperature SrTiO₃ [35,36]. The rate of frequency change with temperature changes abruptly in the temperature range between 670 and 1023 K, i.e. in the orthorhombic Cmcm phase compared to the Pbnm phase of SrHfO₃; this may be related to the distortion of HfO₆ octahedra with displacement of Sr²⁺ ions. This transition is very similar to a displacive phase transition in SrSnO₃ and with the nature of planar ferroelectric domains and the associated real-space correlation function in SrSnO₃ at 905 K near its Pbnm-to-Imma transition [19]. A similar displacive phase transition is also known for the structural phase transition of SrTiO₃ at 105 K [6].

Figures 2 and 3 show anomalies in soft-mode frequencies and damping related to the orthorhombic-orthorhombic $Pnma\text{-}Cmcm$ transition. However, we have not observed a soft mode related to this transition (which suggests that it might be order-disorder). A high-temperature phase sequence in SrHfO₃ using Raman spectroscopy will be reported separately in ref. [37]. Therein, we observed an anomalous change in frequencies and linewidth with temperature in the observed four intense Raman modes at 144, 166, 424 and $599\ \text{cm}^{-1}$ near the transition temperature as reported in ref. [10]; in addition, the higher-frequency modes at 651 and $682\ \text{cm}^{-1}$ which are weak in intensity vanish near 670 K without showing any softening behaviour. In the Pnma space group, Sr and Hf occupy the 4a and 4c Wyckoff notation position and oxygen occupy the 4c and 8d Wyckoff position. This phase transition (from Pnma to Cmcm) takes place in a span of the temperature range ${\sim}670\pm 30\ \text{K}$ due to the continuous rotation of HfO₆ octahedra in SrHfO₃ and the oxygen position changes from 8d to 8f in Wyckoff position. These observations also support an order-disorder phase transition from Pnma to Cmcm in SrHfO₃. A similar phase transition was observed in SrSnO₃ near 600 K (ref. [19]). Note that orthorhombic-orthorhombic phase transitions cannot be ferroelastic (the crystal class must change), so this transition cannot exhibit twinning. Regarding the suggested Pnma to Cmcm transition, our results are not definitive and synchrotron studies are recommended. Since only the oxygen ions move, this is not an ideal system to use X-ray techniques for the space group determination. Neutron studies would also be very useful.

We observed temperature-induced soft phonon modes in SrHfO₃ by Raman spectroscopy. The atomic displacements of two soft-phonon components at $107\ \text{cm}^{-1}$ and $232\ \text{cm}^{-1}$ are analogous to those of E_g and A_g modes of a tetragonal $I4/mcm$ phase of SrTiO₃ which originate from the Brillouin zone boundary R₂₅ mode of a prototypic cubic Pm3m phase. These two lowest soft-phonon mode branches remain underdamped in an orthorhombic phase (Pbnm and Cmcm), and the damping constant increases with temperature according to a previously established but empirical universal scaling theory.

Based on the above discussions, SrHfO₃ is thought to be antiferrodistortive but not ferroelectric below 1023 K [36]. It is a highly displacive transition (not order-disorder) and hence should not cause any amorphous degradation of the material in industrial processing. It is nearly second order and hence should also not produce cracking. By comparison, the orthorhombic-orthorhombic transition at 670 K discussed below is not displacive (no soft mode) and it is not ferroelastic (no stress-strain hysteresis), and so it may affect the degree of ordering in SrHfO₃ gateoxides, without introducing hysteretic strain.

MKS and GS are grateful to UGC India for financial support under the major research project (grant No. 39-869/2010). This work was partially supported by the DOE Grant No. DE-FGD2-08ER46526). MKS acknowledges the INSA Delhi and Japan Society for the Promotion of Science (JSPS) for the financial support of his stay at University of Tsukuba, Japan.